1. INTRODUCTION AND BACKGROUND

The subject of the evolution of the active galactic nucleus (AGN)
population began in the late 1960s with
Schmidt's (1968,
1970)
discoveries that the space
densities of both radio and optically selected quasars increased
significantly with redshift. The effect was
so strong that it was detectable in samples as small as 20 objects. He
developed and applied the V / Vm test for
analyzing the space distribution in his samples and showed
that there was a strong evolution in the space density of quasars toward
higher redshift, increasing by more than a factor of 100 from redshift 0
to 2. This was a striking and unexpected result that posed a question
that is still crucial today -- What causes the sharp decline since
-- z = 2?

In this article I will review and discuss the following subjects:

The techniques used to discover quasars and AGNs,
their selection effects, and the
surveys used to study the evolution of the AGN population.

The general picture of evolution up to 1995, when
the first well-defined, quantitative surveys of the evolution of
high-redshift quasars were published.

The current status of major optical surveys such as
2dF and SDSS.

Radio and X-ray surveys and how they are critical
to understanding AGN evolution.

The relation of AGNs to their host galaxies and how
studies of massive black holes in spheroids provide constraints on AGN
evolution.

Current research problems, such as measuring the
quasar luminosity function at high redshift and faint magnitudes;
relating observed to physical evolution; the
framework for connecting observations, accretion processes, and the
growth of black hole masses; and how to estimate black hole masses.

Before proceeding, let us define and discuss terms used in this article
to aid the clarity of the presentation.

An AGN is one not powered by normal stellar processes,
although active star formation may be occurring in the vicinity. The
working hypothesis is that AGNs contain massive black holes and are
powered by accretion processes. Their
luminosities range from as low as MB = - 9 mag to as
high as MB = - 30 mag (LX =
1038 to 1048 erg s-1).
Quasars are the high-luminosity (MB < - 23 mag,
LX > 1044 erg s-1)
members of the AGN family.

Traditionally, evolution of AGNs or quasars has meant the evolution with
redshift of their luminosity function or space density (which is the
integral of the luminosity function over some range of
luminosities). However, evolution can also refer to changes with
redshift of the spectral energy distribution (SED) or the emission-line
spectra of AGNs. In general, observed evolution will refer to
changes with redshift of any observed property of AGNs.

Ultimately, we wish to map and understand the physical evolution
of AGNs, by which we mean how their central black holes form and grow
with cosmic epoch and how their accretion processes and rates, which
determine the luminosities and SEDs we observe from AGNs, evolve with
cosmic epoch. The discovery of the ubiquity of black holes in the
spheroids of nearby galaxies makes us realize that the physical
evolution of AGNs is closely connected with and is an important part of
the larger subject of how galaxies in general form and evolve. It
appears that virtually every spheroidal system went through an AGN phase
at some time in its history -- thus the subject of our meeting:
"The Coevolution of Black Holes and Galaxies."

However, the persistent question of how many AGNs are hidden because of
weak emission lines, obscuration by dust, or absorption in X-rays has
continued to impede progress in the mapping of the observational
evolution of AGNs and must be addressed in any attempt to determine the
properties of the overall AGN population. Fortunately, the advent of
powerful new space observatories such as Chandra and
XMM-Newton, in conjunction with sensitive radio and infrared
surveys, provides new tools for attacking this problem, as will be
addressed below.

At the same time, the formulation and application of the appropriate
observational
definitions of AGNs continue to be critical issues in current research,
especially for low-luminosity objects,
which can be hard to find within the glare of their host galaxy or to
separate from normal stars. For example, the work of
Ho (2003)
suggests that some AGNs may have X-ray luminosities down to
1036 erg s-1, or less than stellar X-ray sources.

If we are really to understand the global population of AGNs and their
relation to galaxies, these problems must be solved. This will be one of
the themes to be developed in this article.